相关论文: Five Guidelines for Partition Analysis with Applic…

Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…

This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…

Suppose we partition the integers into finitely many cells. Can we always find a solution of the equation $x^2+y^2=z^2$ with $x,y,z$ on the same cell? What about more general homogeneous quadratic equations in three variables? These are…

We revisit several partition-theoretic generating functions, including the theta quotients from Ramanujan's lost notebook, MacMahon's partition functions, and reciprocal sums of parts in partitions, through the lens of the classical Fa\`{a}…

In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a…

A numerical method is proposed to compute a low-rank Galerkin approximation to the solution of a parametric or stochastic equation in a non-intrusive fashion. The considered nonlinear problems are associated with the minimization of a…

We compare different analytical and numerical methods for studying the partitions of a finite system into fragments. We propose a new numerical method of exploring the partition space by generating the Markov chains of partitions based on…

Let $\mathscr{S}$ denote the set of integer partitions into parts that differ by at least $3$, with the added constraint that no two consecutive multiples of $3$ occur as parts. We derive trivariate generating functions of Andrews--Gordon…

Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties,…

We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers-Ramanujan partitions, theta functions, mock theta functions, partitions with…

Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…

The generating function for $p_N(n)$, the number of partitions of $n$ into at most $N$ parts, may be written as a product of $N$ factors. We find the behavior of coefficients in the partial fraction decomposition of this product as $N \to…

Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of…

For rational $\alpha$, the fractional partition functions $p_\alpha(n)$ are given by the coefficients of the generating function $(q;q)^\alpha_\infty$. When $\alpha=-1$, one obtains the usual partition function. Congruences of the form…

Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…

Noting a curious link between Andrews' even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles,…

The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to…

We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive…